Yes. Assuming the lamp was all correctly wired with the proper size cord originally, then using a 13A fuse in the plug in Britain it will just as safe as it was in France. But if there's no reason to need the 13A fuse, then using a smaller one will provide slightly greater protection. What is the actual rating of the lamp (in watts)?
I was always under the impression that France (and many other European countries) adopted 0.75 sq. mm as the minimum size years ago due to running on 16 or 20A circuits and that 0.5 sq. mm is a particularly British/Irish thing, thanks to fused plugs. Last time I checked in the U.K., 0.5 sq. mm flex was still being made for domestic use, but no doubt with so many appliances being sold Europe-wide these days many manufacturers have switched to 0.75 sq. mm.
Maximum 300 watts. To be honest, it's so bright, 100 watts works just as well (I have used both in France).
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